476
R. Ahrens et al.
agglomeration term is presented that is based on the fast Fourier transform (FFT).
The complexity of this algorithm is discussed as well as the number of moments that
can be conserved.
1 Introduction: Modeling of Crystallization Processes with
Population Balance Systems
Solid state processing is an important part of the industrially relevant production
as about 70% of products of the chemical and pharmaceutical industry are sold as
solids. An important part of this processing is crystallization of solid materials from
liquid solutions. Fundamental and applied research in this area of crystallization
will lead to improved process performance with less energy consumption as well
as more efficient material utilization. Also the product quality and specifications
like size and its distribution, shape, and agglomeration degree have to be considered
in more detail, as many process steps are dependent on such characteristics [44].
The DFG priority programme 1679 “Dynamic simulation of interconnected solids
processes” addressed many of the current issues and our particular contribution has
been the investigation of different important aspects of continuous crystallization
processes. As solid-liquid systems are complex and challenging in many ways and
fluid flow and particles interact in a variety of fashions, the numerical methods had
to be extended and new tools had to be developed to simulate crystallization in a
better way. We focus here on relevant phenomena of crystal growth of multi-faceted
crystals as well as on crystal agglomeration with two specifically developed model
experiments working with selected well-understood model substances.
Crystallization processes are often modeled in terms of a crystal population instead
of considering the behavior of each individual crystal. Utilizing macroscopic conservation laws, one derives a system of coupled equations for the population, a so-called
population balance system (PBS), that describes an averaged behavior of the crystals.
We consider crystallization processes within a moving incompressible fluid, which
occur, e.g., in pipes or batch crystallizers. It is assumed that the suspension of the
crystals is dilute such that the impact of the crystals on the fluid flow is negligible.
Then, the first two conservation laws are the balance of the linear momentum and
V. Wiedmeyer
ETH Zurich, Institute of Energy and Process Engineering, Sonneggstrasse 3, 8092 Zurich,
Switzerland
e-mail: wiedmeyv@ipe.mavt.ethz.ch
V. John
Freie Universität Berlin, Department of Mathematics and Computer Science,
Arnimallee 6, 14195 Berlin, Germany
K. Sundmacher
Process Systems Engineering, Max Planck Institute for Dynamics of Complex Technical
Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
R. Ahrens et al.
agglomeration term is presented that is based on the fast Fourier transform (FFT).
The complexity of this algorithm is discussed as well as the number of moments that
can be conserved.
1 Introduction: Modeling of Crystallization Processes with
Population Balance Systems
Solid state processing is an important part of the industrially relevant production
as about 70% of products of the chemical and pharmaceutical industry are sold as
solids. An important part of this processing is crystallization of solid materials from
liquid solutions. Fundamental and applied research in this area of crystallization
will lead to improved process performance with less energy consumption as well
as more efficient material utilization. Also the product quality and specifications
like size and its distribution, shape, and agglomeration degree have to be considered
in more detail, as many process steps are dependent on such characteristics [44].
The DFG priority programme 1679 “Dynamic simulation of interconnected solids
processes” addressed many of the current issues and our particular contribution has
been the investigation of different important aspects of continuous crystallization
processes. As solid-liquid systems are complex and challenging in many ways and
fluid flow and particles interact in a variety of fashions, the numerical methods had
to be extended and new tools had to be developed to simulate crystallization in a
better way. We focus here on relevant phenomena of crystal growth of multi-faceted
crystals as well as on crystal agglomeration with two specifically developed model
experiments working with selected well-understood model substances.
Crystallization processes are often modeled in terms of a crystal population instead
of considering the behavior of each individual crystal. Utilizing macroscopic conservation laws, one derives a system of coupled equations for the population, a so-called
population balance system (PBS), that describes an averaged behavior of the crystals.
We consider crystallization processes within a moving incompressible fluid, which
occur, e.g., in pipes or batch crystallizers. It is assumed that the suspension of the
crystals is dilute such that the impact of the crystals on the fluid flow is negligible.
Then, the first two conservation laws are the balance of the linear momentum and
V. Wiedmeyer
ETH Zurich, Institute of Energy and Process Engineering, Sonneggstrasse 3, 8092 Zurich,
Switzerland
e-mail: wiedmeyv@ipe.mavt.ethz.ch
V. John
Freie Universität Berlin, Department of Mathematics and Computer Science,
Arnimallee 6, 14195 Berlin, Germany
K. Sundmacher
Process Systems Engineering, Max Planck Institute for Dynamics of Complex Technical
Systems, Sandtorstr. 1, 39106 Magdeburg, Germany